{
  "id": 2902,
  "curve_key": "4445398343802136679446172161:295754235336444020460063145037341799548159",
  "ainvs": [
    "1",
    "1",
    "1",
    "-92612465495877847488461920",
    "-342308142750552501096807478081525053055"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2,
    2
  ],
  "naive_height": 190.98500097582982,
  "faltings_height": 13.717608643190722,
  "conductor": "548088118837830139058490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "29",
    "31",
    "37",
    "47",
    "59",
    "61",
    "349",
    "21269"
  ],
  "discriminant": "218441540503697394418566348625991914474920432200623399026711965906221415040000",
  "regulator": "1965606.217744365299818339264942494843646289636127023",
  "points": [
    [
      "-5564460649447",
      "858283024373587233"
    ],
    [
      "28417212774053",
      "-141329000524103357787"
    ],
    [
      "-464983321725995/81",
      "295986921239440592621/729"
    ],
    [
      "-5425744871467",
      "675688434102402453"
    ],
    [
      "-50810162552573/9",
      "20980234717329380251/27"
    ],
    [
      "-48175093165955/9",
      "6437956080208839223/27"
    ],
    [
      "25430074808813",
      "-117251418131252685387"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2z4old678-067, rational kernel x=2882616151573. Source: https://dujella.github.io/tors/z2z4old678.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.",
  "created_at": "2026-09-26 20:27:37",
  "updated_at": "2026-09-26 20:27:37"
}